Basically: hair, face shape, eyes. The first two work in combination for a silhouette, so at a minor glance you can tell the character without the details filled in (this is encouraged in concept art, especially for games). Hair styling can give personality, culture, and preferences - even messy hair vs immaculate hair says something. Hair might not be the face, but in reality we look at most of the head when we ID a character, and the hair helps set and frame the face, so don't ignore that.

Shape might be dictated by art-style (as in most Sailor Moon characters have very similar shapes without much variation), but if it isn't held back in yours then I suggest trying minor alterations to the face shape. More square or round or pointed, long or squat, pudgy or gaunt, and all the phases between. This also includes cheekbones, chins, and jawbones. Noses sometimes get set to the "generic nose" for ease of drawing, especially for comics and shows that are churned out quickly, but they can be very defining features that set characters apart too. In combination you can see the character's personality come out - Snape's gaunt, long face with hookish nose tells you quite a bit about him, doesn't it?

Eyes. Minor adjustment in eyes can really help. Shape (round or almond, or in between), length, spacing, height, size, and folds give you a lot about a character - race perhaps, but also personality and emotional state. Narrow eyes are suspicious, beady shrewd, wide innocent.

You'll note I brought up "personalty" and emotional stuff a lot. That will dictate quite a bit on what changes you can make. They can even look very average - some genericness is not terrible, remember "nihil novi sub sole," "nothing is new under the sun." A few alterations can make a face look similar to a generic one (because their personalty leans toward that, hence generic faces that pop up in comic and animation mediums), but still stands out on its own. Even my Vale looks similar to a certain style of dark or snarky character, but has his own thing going here and there. Find something that would draw your character's personality out to a reader in a feature. Great example to me: Brienne of Tarth's description from various PoVs in the A Song of Ice and Fire novels note her lack of feminine features and roughness, but her eyes stand out to nearly everyone that really looks at them, and they reflect so much about her personality and about the people that spend time to really describe them.

So find that major personality point that really reflects this character, and think of a feature that could give a viewer a slight bit of insight into that character. Sorry if those suggestions feel generic themselves, or difficult to work from - it isn't easy to convey off the bat and can take a lot of redraws until you "find it," and practice to consistently keep whatever that is you found. Hope that gives you a little direction - all you need will be in the character's own self, oddly enough. And they need not be major changes either!

Thanks. The advice really does help. Art is not something I'm good at, as I've never invested time in it. I'm using a site that allows you to use and resize fre-fab elements to create a character, so there are some limitations. But still, good suggestions, overall. I might end up looking through photos to find one that matches the personality well, and base it off that.